Freron MailMate

I am seeing two behaviors with tags and Gmail that are not great, although not fatal, either.

First, if I tag an email in MailMate, and then go to the Tags preference panel and give that tag a Gmail equivalent, MailMate removes the tag from all emails with that tag. I am not touching the Display or IMAP Keyword column, merely typing something into the gmail column, and the original tag goes poof. If I re-apply the tag, it sticks, and properly tags on Gmail as well.

Second, I am not getting gmail (web client) to Mailmate tag syncing unless I also change the tags on the MailMate side. That is, when I make a tag change on MailMate, it appears on Gmail as well (presuming I have filled in the Gmail column in the tags preference panel). But when I make a change on the Gmail side, using the Gmail web app, the revision doesn't appear on MailMate. I can sync the account, quit and restart Mailmate, open the email, the Gmail tag revision does not appear. Only if I make a change to the tags for that email using MailMate (any change, not necessarily duplicating the change I made on Gmail) does it re-sync with Gmail.

Perhaps these are both working as intended, but they are annoying and potentially problematic in my workflow, so if there is a way I can avoid this problems, I would be grateful to have it pointed out. I am subscribed to Gmail/All Mail, as recommended in the manual, but both these problems existed before and after I subscribed.